Question

The time period of oscillation of a bar magnet suspended horizontally along the magnetic meridian is T${}_0$ . If this magnet is replaced by another magnet of the same size and pole strength, but with double the mass, the new time period will be :

• A. $\frac{T_0}{2}$
• B. $\frac{T_0}{\sqrt{2}}$
• C. $\sqrt{2}{T}_0$
• D. $2T_0$

Answer 1

The correct option is C $\sqrt{2}{T}_0$

$\because T=2\pi \sqrt{\frac{I}{me}}$ $(m=magneticmomentI=m{r}^{2}B=magneticfreed)$

$\Rightarrow T_0=2\pi \sqrt{\frac{{mr}^2}{mB}}$

$\Rightarrow T^{\prime }=2\pi \sqrt{\frac{{2mr}^2}{mB}}$

$\Rightarrow \frac{T^{\prime }}{T_0}=2\pi \sqrt{\frac{{2mr}^2}{mB}}\times \frac{1}{2\pi }\sqrt{\frac{mB}{{mr}^2}}$

$\Rightarrow T^{\prime }=T_0\sqrt{2}$

Hence, the answer is $\sqrt{2}{T}_0.$